A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Publisher Summary The widespread availability of spatially and temporally coherent laser sources makes the production of optical vortices inevitable in any experiment involving scattered laser light. The realization of quantized vortices is not specific to optics: these objects occur in all spatial scalar fields. Although optical vortices are often referred to as “points of phase singularity within a cross section of the field,” physical optical fields extend over three dimensions, and the phase singularities are actually lines of perfect destructive interference that are embedded in the volume filled by the light. Optical vortices are examples of the singularity lines within all complicated scalar fields. By comparison, electromagnetic vector fields do not generally have nodes in all components simultaneously. However, vector fields possess singularities associated with the parameterization of elliptical and partial polarization rather than phase. Polarization singularities are present in many situations, ranging from sunlight to the light transmitted by birefringent materials. Their descriptors are more complicated than their scalar counterpart in that they have both handedness and additional categorization. The study of optical vortices and orbital angular momentum has led to a recognition that the energy flow—characterized by the Poynting vector—has features not immediately apparent from the intensity alone, nor from global properties of a beam.

Singular optics: optical vortices and polarization singularities

The effects of propagation through random aberrations on coherence for single-photon communication systems based on orbital angular momentum states are quantified. A rotational coherence function is derived which leads to scattering equations for azimuthal modes of different orbital angular momentum states. The effect on a single-photon communication system is quantified using the channel capacity. The work shows that the decoherence effect of atmospheric turbulence on such systems is important even for weak turbulence.

Atmospheric turbulence and orbital angular momentum of single photons for optical communication.

Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review

Interferometric optical profilers deliver non-contact, fast, full-field measurements with vertical resolution down to a fraction of a nanometer. Over the last decade advancements to these instruments have allowed for the analysis of not only static but also dynamic objects, like cantilevers and other microelectromechanical system devices, moving or vibrating at up to 1 MHz frequencies. Special objectives and illumination allow for imaging and testing of objects enclosed in environmental or protective chambers or immersed in liquids—including biological samples. Advanced analysis of the interference signal allows for the measurement not just of the surface profile but also transparent coatings.

https://iopscience.iop.org/article/10.1088/1464-4258/10/6/064001/pdf

Performance advances in interferometric optical profilers for imaging and testing

White-light interferometry (WLI) for object topography measurements relies on an accurate rate of change of the optical path difference (OPD) between the object and reference beams. However, the motion of the scanner realizing the OPD change is not perfect, and scanning errors directly impact measurement accuracy. We describe a white-light interferometer that is capable of accounting for these errors and correcting them in real time through the monitoring of the scanner motion. This monitoring is achieved by embedding an additional high-coherence interferometer into the system. Besides allowing for monitoring the scanning progress, this system also provides the means to automatically calibrate the WLI. Significant improvements both in the accuracy and repeatability are demonstrated experimentally. Data analysis is discussed as well.

High-stability white-light interferometry with reference signal for real-time correction of scanning errors

Interference measurements of a polychromatic partially coherent light source verify the existence of a temporal correlation vortex. Topological dispersion is found to destabilize this singularity.

https://www.cis.rit.edu/~grovers/Doc/Publications/PRL_Schmit.pdf

Temporal correlation vortices and topological dispersion.

The dynamic nanomechanical properties of a large number of cells (up to hundreds), measured in parallel with high throughput, are reported. Using NIH 3T3 and HEK 293T fibroblasts and actin depolymerizing drugs, we use a novel nanotechnology to quantify the local viscoelastic properties with applied forces of 20 pN–20 nN, a spatial resolution of <20 nm, and a mechanical dynamic range of several Pa up to ~200 kPa. Our approach utilizes imaging interferometry in combination with reflective, magnetic probes attached to cells. These results indicate that mechanical imaging interferometry is a sensitive and scalable technology for measuring the nanomechanical properties of large arrays of live cells in fluid.

/pdf/high-throughput-cell-nanomechanics-with-mechanical-imaging-2s2kys8o3n.pdf

High throughput cell nanomechanics with mechanical imaging interferometry.

Spectrally resolved white-light phase-shifting interference microscopy can be used for rapid and accurate measurements of the thickness profile of transparent thin-film layers deposited upon patterned structures exhibiting steps and discontinuities. We examine the sensitivity of this technique and show that it depends on the thickness of the thin-film layer as well as its refractive index. The results of this analysis are also valid for any other method based on measurements of the spectral phase such as wavelength scanning or white-light interferometry.

Joanna Schmit

Papers

Performance advances in interferometric optical profilers for imaging and testing

High-stability white-light interferometry with reference signal for real-time correction of scanning errors

Temporal correlation vortices and topological dispersion.

High throughput cell nanomechanics with mechanical imaging interferometry.

Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements.